1. Field of the Invention
The invention relates generally to PSK-modulated space-time codes, and more particularly, to the method and construction of space-time codes for AM-PSK constellations.
2. Description of the Related Art
Recent advances in coding theory include space-time codes which provide diversity in multiple-input multiple-output (MIMO) antenna systems over fading channels with channel coding across a small number of transmit antennas. For wireless communication systems, a number of challenges arise from the harsh RF propagation environment characterized by channel fading and co-channel interference (CCI). Channel fading can be attributed to diffuse and specular multipath, while CCI arises from reuse of radio resources. Interleaved coded modulation on the transmit side of the system and multiple antennas on the receive side are standard methods used in wireless communication systems to combat time-varying fading and to mitigate interference. Both are examples of diversity techniques.
Simple transmit diversity schemes (in which, for example, a delayed replica of the transmitted signal is retransmitted through a second, spatially-independent antenna and the two signals are coherently combined at the receiver by a channel equalizer) have also been considered within the wireless communications industry as a method to combat multipath fading. From a coding perspective, such transmit diversity schemes amount to repetition codes and encourage consideration of more sophisticated code designs. Information-theoretic studies have demonstrated that the capacity of multi-antenna systems significantly exceeds that of conventional single-antenna systems for fading channels. The challenge of designing channel codes for high capacity multi-antenna systems has led to the development of “space-time codes,” in which coding is performed across the spatial dimension (e.g, antenna channels) as well as time.
Space-time codes are designed for MIMO communication systems that employ multiple transmit antennas to achieve spatial diversity. The modulated code words are often presented as complex-values M×T matrices in which the (m,t)-th entry sm,t represents the discrete baseband signal transmitted from the m-th transmit antenna at time t. The initial work on space-time codes by Guey et al. and Tarokh et al. showed that the transmit diversity achieved by a space-time code is equal to the minimum rank among the set of matrices produced as differences between distinct modulated code words. There is a tradeoff between achievable transmission rate and achievable transmit diversity level for space-time codes. Full-rank space-time codes can achieve transmission rates no greater than one symbol per transmission interval. For rank d space-time codes, the maximum transmission rate is M−d+1 symbols per transmission interval. Equivalently, the size of an M×T rank-d space-time code cannot exceed qT(M−d+1), where q is the size of the signaling constellation. Codes meeting this upper limit are referred to as maximal.
In U.S. Pat. No. 6,678,263, Hammons and El Gamal developed the so-called binary rank criteria that allowed, for the first time, the algebraic design of space-time codes achieving maximal spatial diversity of all orders. The binary rank criteria for BPSK- and QPSK-modulated space-time codes are based on the observation that the difference between two modulated code words will be of full rank, as a matrix over the complex field C, whenever a certain binary projection of the difference matrix is of full rank over the binary field GF(2). From the binary rank criteria, Hammons and El Gamal developed the general Stacking Construction for full-diversity space-time codes, examples of which include block codes derived from Galois fields/rings and rate 1/M convolutional codes of optimal dfree. The binary rank criteria showed that the algebraically-designed, full-rank, BPSK-modulated space-time codes could be lifted to full-rank, QPSK-modulated space-time codes. In particular, Hammons and El Gamal showed that, if the linear binary codes A and B produce full-rank space-time codes when BPSK modulated, then the quaternary code C=A+2B produces a full-rank space-time code under QPSK modulation. They referred to this construction as the Dyadic Construction.
Building on the Hammons-El Gamal framework, Liu et al. showed how the same techniques could be extended to 4m-QAM constellations. Thereafter, Lu and Kumar developed a generalization of that framework applicable to both the 4m-QAM and the general 2m-PSK cases. They showed that the Dyadic Construction extends to 2m-PSK modulation in the natural way—i.e., if the linear binary codes A0, A1, . . . , Am-1 produce full-rank space-time codes under BPSK modulation, then the 2m-ary code
  C  =            ∑              i        =        0                    m        -        1              ⁢                  2        i            ⁢                          ⁢              A        i            produces a full-rank space-time code under 2m-PSK modulation. They showed that similar results apply to codes of rank d (less than full rank). Finally, Lu and Kumar provided a unified space-time code construction extending the Dyadic Construction for 2m-PSK modulation to include natural codes for 4m-QAM modulation. They proved that their unified space-time code construction is optimal for these modulations in the sense that it achieves the aforementioned rate-diversity tradeoff.
Dual radii AM-PSK constellations offer potential significant advantages over conventional PSK constellations. For example, Belzer et al. show that the 8-ary AM-PSK constellation consisting of two PQSK rings in a star configuration provides significantly higher capacity on partially coherent AWGN, Rayleigh, and Rician fading channels. However, nothing in the prior art teaches the development of general space-time code constructions for AM-PSK constellations or the unification of such constructions with the Lu-Kumar space-time codes for PSK and QAM constellations. Accordingly, it would be desirable to be able to utilize space-time code constructions for AM-PSK constellations, especially such codes that are optimal with respect to the rate-diversity tradeoff.